Best Known (112, 141, s)-Nets in Base 4
(112, 141, 1055)-Net over F4 — Constructive and digital
Digital (112, 141, 1055)-net over F4, using
- 41 times duplication [i] based on digital (111, 140, 1055)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (10, 24, 27)-net over F4, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 10 and N(F) ≥ 27, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- digital (87, 116, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 29, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 29, 257)-net over F256, using
- digital (10, 24, 27)-net over F4, using
- (u, u+v)-construction [i] based on
(112, 141, 4367)-Net over F4 — Digital
Digital (112, 141, 4367)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4141, 4367, F4, 29) (dual of [4367, 4226, 30]-code), using
- 257 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 11 times 0, 1, 18 times 0, 1, 27 times 0, 1, 40 times 0, 1, 58 times 0, 1, 80 times 0) [i] based on linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 257 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 11 times 0, 1, 18 times 0, 1, 27 times 0, 1, 40 times 0, 1, 58 times 0, 1, 80 times 0) [i] based on linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using
(112, 141, 2113168)-Net in Base 4 — Upper bound on s
There is no (112, 141, 2113169)-net in base 4, because
- 1 times m-reduction [i] would yield (112, 140, 2113169)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 1 942676 904917 736902 846808 082656 039923 485445 880826 969442 833864 893591 534897 188924 680120 > 4140 [i]